## Automating access control logics in simple type theory with LEO-II (2008)

Venue: | FB Informatik, U. des Saarlandes |

Citations: | 11 - 9 self |

### BibTeX

@TECHREPORT{Benzmüller08automatingaccess,

author = {Christoph Benzmüller},

title = {Automating access control logics in simple type theory with LEO-II},

institution = {FB Informatik, U. des Saarlandes},

year = {2008}

}

### OpenURL

### Abstract

Abstract Garg and Abadi recently proved that prominent access control logics can be translated in a sound and complete way into modal logic S4. We have previously outlined how normal multimodal logics, including monomodal logics K and S4, can be embedded in simple type theory and we have demonstrated that the higher-order theorem prover LEO-II can automate reasoning in and about them. In this paper we combine these results and describe a sound (and complete) embedding of different access control logics in simple type theory. Employing this framework we show that the off the shelf theorem prover LEO-II can be applied to automate reasoning in and about prominent access control logics. 1

### Citations

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Citation Context ...translated into modal logic S4 [18]. They proved that this translation is sound and complete. We have previously shown [10] how multimodal logics can be elegantly embedded in simple type theory (STT) =-=[15, 5]-=-. We have also demonstrated that proof probChristoph Benzmüller International University in Germany, Bruchsal, Germany, e-mail: c.benzmueller@ googlemail.com ∗ This work was supported by EU grant PIIF... |

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Citation Context ...translated into modal logic S4 [18]. They proved that this translation is sound and complete. We have previously shown [10] how multimodal logics can be elegantly embedded in simple type theory (STT) =-=[15, 5]-=-. We have also demonstrated that proof probChristoph Benzmüller International University in Germany, Bruchsal, Germany, e-mail: c.benzmueller@ googlemail.com ∗ This work was supported by EU grant PIIF... |

185 |
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Citation Context ...gherorder theorem prover LEO-II [12]. In this paper we combine the above results and show that different access control logics can be embedded in STT, which has a well understood syntax and semantics =-=[22, 4, 3, 9]-=-. The expressiveness of STT furthermore enables the encoding of the entire translation from access control logic input syntax to STT in STT itself, thus making it as transparent as possible. Our embed... |

155 |
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Citation Context ... first. He presents an embedding of modal logic into a 2-sorted type theory. This idea is picked up by Gamut [17] and a related embedding has recently been studied by Hardt and Smolka [20]. Carpenter =-=[14]-=- proposes to use lifted connectives, an idea that is also underlying the embeddings presented by Merz [24], Brown [13], Harrison [21, Chap. 20], and Kaminski and Smolka [23]. In our previous work [10]... |

135 | E – A Brainiac Theorem Prover
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Citation Context ...mulated in control logics ICL, ICL ⇒ , or ICL B to problems in STT and we can apply the off the shelf higher-order theorem prover LEO-II (which itself cooperates with the first-order theorem prover E =-=[25]-=-) to solve them. Times are given in seconds. Table 1 shows that LEO-II can effectively prove that the axioms unit, cuc and idem hold as expected in our embedding of ICL in STT. This provides additiona... |

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Citation Context ...arly, s= βηt means s can be converted to t using both β and η. Semantics of STT is well understood and thoroughly documented in the literature [9, 3, 4, 22]; our summary below is adapted from Andrews =-=[6]-=-. A frame is a collection {Dα}α∈T of nonempty domains (sets) Dα, such that Do = {T,F} (where T represents truth and F represents falsehood). The D α→β are collections of functions mapping Dα into D β ... |

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Citation Context ...nt to effectively control the access to personalized or security critical files. A prominent and successful approach to implement access control relies on logic based ideas and tools. Abadi’s article =-=[2]-=- provides a brief overview on the frameworks and systems that have been developed under this approach. Garg and Abadi recently showed that several prominent access control logics can be translated int... |

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38 | LEO-II—a cooperative automatic theorem prover for higher-order logic
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Citation Context ...This work was supported by EU grant PIIF-GA-2008-219982 (THFTPTP). 12 Christoph Benzmüller lems in and about multimodal logics can be effectively automated with the higherorder theorem prover LEO-II =-=[12]-=-. In this paper we combine the above results and show that different access control logics can be embedded in STT, which has a well understood syntax and semantics [22, 4, 3, 9]. The expressiveness of... |

35 |
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Citation Context ...gherorder theorem prover LEO-II [12]. In this paper we combine the above results and show that different access control logics can be embedded in STT, which has a well understood syntax and semantics =-=[22, 4, 3, 9]-=-. The expressiveness of STT furthermore enables the encoding of the entire translation from access control logic input syntax to STT in STT itself, thus making it as transparent as possible. Our embed... |

34 |
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Citation Context ...gherorder theorem prover LEO-II [12]. In this paper we combine the above results and show that different access control logics can be embedded in STT, which has a well understood syntax and semantics =-=[22, 4, 3, 9]-=-. The expressiveness of STT furthermore enables the encoding of the entire translation from access control logic input syntax to STT in STT itself, thus making it as transparent as possible. Our embed... |

33 | A modal deconstruction of access control logics
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(Show Context)
Citation Context ... overview on the frameworks and systems that have been developed under this approach. Garg and Abadi recently showed that several prominent access control logics can be translated into modal logic S4 =-=[18]-=-. They proved that this translation is sound and complete. We have previously shown [10] how multimodal logics can be elegantly embedded in simple type theory (STT) [15, 5]. We have also demonstrated ... |

25 |
Tps: A hybrid automatic-interactive system for developing proofs
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Citation Context ...submitted to the higher-order TPTP library [1] under development in the EU project THFTPTP and are available there for comparison and competition with other TPTP compliant theorem provers such as TPS =-=[7]-=-. Recent experiments have shown that the scalability of our approach for reasoning within access control logics still poses a challenge to LEO-II. However, more promising is the application of LEO-II ... |

18 |
Higher Order Semantics and Extensionality
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Citation Context |

13 | THF0 — the core TPTP language for classical higher-order logic
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Citation Context ...nd examples presented in Section 3. In a separate technical report [8] we present the concrete encoding or our embedding together with the problems unit, cuc, idem, and Ex1 in the new TPTP THF syntax =-=[11]-=-, which is also the input syntax of LEO-II. 6 See Theorem 8 of Garg and Abadi [18] which is only given in the full version of the paper available from http://www.cs.cmu.edu/ ∼ dg/publications.html.Au... |

12 | Exploring properties of normal multimodal logics in simple type theory with LEO-II - Benzmüller, Paulson |

9 | Higher-order syntax and saturation algorithms for hybrid logic
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Citation Context ...mention the idea first. He presents an embedding of modal logic into a 2-sorted type theory. This idea is picked up by Gamut [17] and a related embedding has recently been studied by Hardt and Smolka =-=[20]-=-. Carpenter [14] proposes to use lifted connectives, an idea that is also underlying the embeddings presented by Merz [24], Brown [13], Harrison [21, Chap. 20], and Kaminski and Smolka [23]. In our pr... |

9 | Terminating tableaux for hybrid logic with the difference modality and converse
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Citation Context ...and Smolka [20]. Carpenter [14] proposes to use lifted connectives, an idea that is also underlying the embeddings presented by Merz [24], Brown [13], Harrison [21, Chap. 20], and Kaminski and Smolka =-=[23]-=-. In our previous work [10] we pick up and extend the embedding of multimodal logics into STT as studied by Brown [13]. The starting point is a characterization of multimodal logic formulas as particu... |

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Citation Context ...g Modal Logic in Simple Type Theory Embeddings of modal logics into higher-order logic have not yet been widely studied, although multimodal logic can be regarded as a natural fragment of STT. Gallin =-=[16]-=- appears to mention the idea first. He presents an embedding of modal logic into a 2-sorted type theory. This idea is picked up by Gamut [17] and a related embedding has recently been studied by Hardt... |

3 |
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Citation Context ...a related embedding has recently been studied by Hardt and Smolka [20]. Carpenter [14] proposes to use lifted connectives, an idea that is also underlying the embeddings presented by Merz [24], Brown =-=[13]-=-, Harrison [21, Chap. 20], and Kaminski and Smolka [23]. In our previous work [10] we pick up and extend the embedding of multimodal logics into STT as studied by Brown [13]. The starting point is a c... |

2 |
Festschrift in honour of Peter B. Andrews on his 70th birthday. Studies in Logic and the Foundations of Mathematics, chapter Exploring Properties of Normal Multimodal Logics in Simple Type Theory with LEO-II
- Benzmüller, Paulson
- 2008
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Citation Context ...rg and Abadi recently showed that several prominent access control logics can be translated into modal logic S4 [18]. They proved that this translation is sound and complete. We have previously shown =-=[10]-=- how multimodal logics can be elegantly embedded in simple type theory (STT) [15, 5]. We have also demonstrated that proof probChristoph Benzmüller International University in Germany, Bruchsal, Germa... |

2 | HOL Light Tutorial (for version 2.20). Intel JF1-13, 2011. Section 18.2: Fermat’s Little Theorem - Harrison |

2 |
Yet another encoding of TLA
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Citation Context ...ut [17] and a related embedding has recently been studied by Hardt and Smolka [20]. Carpenter [14] proposes to use lifted connectives, an idea that is also underlying the embeddings presented by Merz =-=[24]-=-, Brown [13], Harrison [21, Chap. 20], and Kaminski and Smolka [23]. In our previous work [10] we pick up and extend the embedding of multimodal logics into STT as studied by Brown [13]. The starting ... |

2 | Intensional Logic and Logical Grammar, volume 2. The University of - Logic, Volume - 1991 |

2 | The file ICL_s4.ax provides the axioms R and T are added to to obtain a mapping into modal logic S4. %------------------------------------------------------------------------------ % File : ICL_s4.ax % Domain : ICL Logic and its translation into Modal Log - Paulson |

2 | File ICL_ex1_s4.thf contains the encoding of Example 1. %------------------------------------------------------------------------------ % File : ICL_ex1_s4.thf % Domain : ICL Logic and its translation into Modal Logic (which is % itself modeled in simple - Paulson |

2 | ICL_idem_s4.thf contain the encodings of the axioms unit, cuc and idem as proof problems. %------------------------------------------------------------------------------ % File : ICL_unit_s4.thf % Domain : ICL Logic and its translation into Modal Logic S4 - thf, thf |

2 | http://www.ags.uni-sb.de/~chris/papers/B9.pdf % Status : Theorem (Henkin semantics) % Syntax : % Comments : Formalization in THF by C. Benzmueller %------------------------------------------------------------------------------ include(’ICL_k.ax’). include - See |

1 | 7 TPTP THF Problem files for Ex1 The file ICL_k.ax presents the general definitions of our mapping from access control logics via modal logic K to STT. %---------------------------------------------------- % File : ICL_k.ax % Domain : ICL Logic and its tr - Benzmueller, Paulson |